We're looking at a closed system.
We know the entropy inside it can only ever increase, which, according to the Gibbs-Helmholtz formula G = H-T*S inevitably leads to the decrease of free energy until it reaches a level too low to sustain life.

In short, though this system can sustain itself for very long time, it is inevitably doomed from the moment the cork is put in.
Kinda depressing.

Theoretically it's possible; what we call "age" is a bunch of cellular defects accumulating until they kill you.
All of those defects could be reversed in theory, there is no reason any life-form cannot be made to have an unlimited life-expectancy.
Our only problem is that we don't have the technology yet.

A guy called Aubrey deGrey heads a project about exactly this, you might wanna check it out if you like this kind of stuff.
Even though the guy's kinda weird, his work is fascinating.